Turbulent characteristics in wall-wake flows downstream of wall-mounted and near-wall cylinders are investigated. The distributions of the defect of streamwise velocity, Reynolds shear stress and turbulence intensities exhibit a certain degree of self-preserving characteristic when they are scaled by their respective peak defect values. For the velocity defect distributions, the vertical distances are scaled by the half-width of peak defect velocity. However, for the distributions of the defects of the Reynolds shear stress and the turbulence intensities, the vertical distances are scaled by the half-width of Reynolds shear stress defect. The peak defects of all the quantities reduce with longitudinal distance signifying the recovery of the upstream distributions of the individual quantities. The third-order correlations reveal that for the wall-mounted cylinder, a streamwise acceleration associated with a downward flux of streamwise Reynolds normal stress (SRNS) in the inner-layer of wall-wake composes sweeps and a streamwise deceleration associated with an upward flux of SRNS in the outer-layer forms ejections. On the other hand, for the near-wall cylinder, a streamwise deceleration associated with a downward flux of SRNS in the inner-layer of wall-wake flow and the gap flow produces the inward interaction events, while the outer-layer characteristic is similar to that of wall-mounted cylinder. The turbulent kinetic energy (TKE) budget in the wake flow demonstrates strong negative pressure energy diffusion in addition to a strong TKE dissipation and diffusion and that in the gap flow exhibits a minor positive peak of pressure energy diffusion and a minor negative peak of TKE diffusion. © 2018, Springer Science+Business Media B.V., part of Springer Nature.